Find the area of a ring shaped region enclosed between two concentric circles of radii 20 cm and 15 cm.

Answer

To find the area of the ring-shaped region enclosed between two concentric circles with radii 20 cm and 15 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Radii of the Circles:**
- The radius of the larger circle (R) = 20 cm
- The radius of the smaller circle (r) = 15 cm

2. **Calculate the Area of the Larger Circle:**
- The formula for the area of a circle is given by:
\[ \text{Area} = \pi R^2 \]
- Substituting the radius of the larger circle:
\[ \text{Area of larger circle} = \pi (20)^2 = \pi \times 400 = 400\pi \text{ cm}^2 \]

3. **Calculate the Area of the Smaller Circle:**
- Using the same formula for the area of a circle:
\[ \text{Area of smaller circle} = \pi r^2 \]
- Substituting the radius of the smaller circle:
\[ \text{Area of smaller circle} = \pi (15)^2 = \pi \times 225 = 225\pi \text{ cm}^2 \]

4. **Find the Area of the Ring-Shaped Region:**
- The area of the ring-shaped region is the difference between the area of the larger circle and the area of the smaller circle:
\[ \text{Area of ring} = \text{Area of larger circle} - \text{Area of smaller circle} \]
- Substituting the areas calculated:
\[ \text{Area of ring} = 400\pi - 225\pi = (400 - 225)\pi = 175\pi \text{ cm}^2 \]

5. **Calculate the Numerical Value of the Area:**
- Using the approximation \(\pi \approx \frac{22}{7}\):
\[ \text{Area of ring} = 175\pi \approx 175 \times \frac{22}{7} \]
- Simplifying:
\[ = \frac{175 \times 22}{7} = \frac{3850}{7} \approx 550 \text{ cm}^2 \]

### Final Answer:
The area of the ring-shaped region is approximately **550 cm²**.